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Axioms 2013, 2(1), 20-43; doi:10.3390/axioms2010020
Article

Some Modular Relations Analogues to the Ramanujan’s Forty Identities with Its Applications to Partitions

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Received: 1 November 2012 / Revised: 22 January 2013 / Accepted: 28 January 2013 / Published: 18 February 2013
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Abstract

Recently, the authors have established a large class of modular relations involving the Rogers-Ramanujan type functions J(q) and K(q) of order ten. In this paper, we establish further modular relations connecting these two functions with Rogers-Ramanujan functions, Göllnitz-Gordon functions and cubic functions, which are analogues to the Ramanujan’s forty identities for Rogers-Ramanujan functions. Furthermore, we give partition theoretic interpretations of some of our modular relations.
Keywords: Rogers-Ramanujan functions; theta functions; partitions; colored partitions; modular relations Rogers-Ramanujan functions; theta functions; partitions; colored partitions; modular relations
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Adiga, C.; Bulkhali, N.A.S. Some Modular Relations Analogues to the Ramanujan’s Forty Identities with Its Applications to Partitions. Axioms 2013, 2, 20-43.

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